A more general framework, able to take into account all the possible constraints and to provide a deeper picture of the metabolic state of the culture comes through the Maximum Entropy Principle (\(ME\) ) [1]}.
This framework has been recently used to model the phenotypic distribution of cells in culture for several growth conditions and cultivation regimes [2]}, [3]}.
In the context of our constraint-based model, the Maximum Entropy Principle may be formulated as follows:
\(\text{maximize arg}_{\mathcal {P}} ~\bigg [-\int _{\mathbb {V}} \mathcal {P}({v}) log(\mathcal {P}({v}))d{v}~\bigg ] \\\text{subject to:} \nonumber \\{v}\in \mathbb {V}\nonumber \\\bar{{v}}= \int _{\mathbb {V}}{v}\mathcal {P}({v}) d{v}\in \bar{\mathbb {V}}\nonumber \) 
